Final answer:
By using elimination, we manipulated the given equations to eliminate one variable and solved for the other, finding the solution x = 1.5 and y = 1.5. We verified the solution by substituting these values back into the original equations.
Step-by-step explanation:
To solve the system of equations using elimination, we need to manipulate the equations to eliminate one of the variables. We are given two equations:
- 6x + 4y = 15
- 4x + 10y = 21
To eliminate one variable, we can multiply the first equation by -5 and the second equation by 2, which will give us coefficients for y that are negatives of each other.
-5(6x + 4y) = -5(15)
2(4x + 10y) = 2(21)
This simplifies to:
-30x - 20y = -75
8x + 20y = 42
Adding these two new equations together, we can eliminate the y variable:
-30x - 20y + 8x + 20y = -75 + 42
Which simplifies to:
-22x = -33
Dividing both sides by -22 gives us x:
x = 1.5
Substituting x back into one of the original equations, let's use the first equation:6(1.5) + 4y = 15
9 + 4y = 15
Subtracting 9 from both sides, we get:
4y = 6
And dividing by 4, we find y:
y = 1.5
Therefore, the solution to the system of equations is x = 1.5 and y = 1.5.
Always check your solutions by substituting them back into the original equations to verify that they satisfy both equations.